Homework Help: math :] 2

Posted by LILY on Monday, February 18, 2008 at 2:19pm.

Is 14/3 a rational number? I think so... but I'm confused because if you divide 14 by 3 then the decimal part is .66666666666666666666667. Is that considered a repeating decimal? If it is, then it's a rational number. I'm just doubting because of the 7 at the end. THANKS SO MUCH!!! =D

math :] 2 - Reiny, Monday, February 18, 2008 at 2:28pm
nothing to be confused about.
Your calculator has a build-in function which rounds off the last decimal it can display, that's why it shows up as a 7

When you do a long division, the way it was taught to you in earlier grades, the 6 will keep on repeating forever.
- math :] 2 - LILY, Monday, February 18, 2008 at 2:33pm
  So is it a national number or what?
  - math :] 2 - LILY, Monday, February 18, 2008 at 2:34pm
    I meant rational, so sorry.
    - math :] 2 - Reiny, Monday, February 18, 2008 at 2:50pm
      yes it is a rational number since it can be written as a fraction, or a RATIO.
      - math :] 2 - LILY, Monday, February 18, 2008 at 2:53pm
        thank you so muchhhhhhhh. =]
math :] 2 - Damon, Monday, February 18, 2008 at 7:43pm
Ah, not to beat a dead horse here but let's make sure the cart is before that horse. The real point is that 14/3 is a RATIO of whole numbers as Reiny capitalized.
That is what makes it a rational number.
The fact that it is a repeating decimal means that it can be written as a ratio, and therefore is rational.
In other words
If ratio, then rational
If repeating decimal, then ratio
Therefore
If repeating decimal, then rational

I suspect shortly you will be shown how to find the ratio that corresponds to any repeating decimal.

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